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Beliebt Rechnen >

derivative of sin(2xcos(3x))

Lösung

\frac{d}{d x} (sin (2 x) cos (3 x))

Lösung

2 cos (2 x) cos (3 x) - 3 sin (3 x) sin (2 x)

Schritte zur Lösung

\frac{d}{d x} (sin (2 x) cos (3 x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (2 x), g = cos (3 x)

= \frac{d}{d x} (sin (2 x)) cos (3 x) + \frac{d}{d x} (cos (3 x)) sin (2 x)

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= cos (2 x) \cdot 2 cos (3 x) + (- sin (3 x) \cdot 3) sin (2 x)

Vereinfache

= 2 cos (2 x) cos (3 x) - 3 sin (3 x) sin (2 x)

Graph

Beliebte Beispiele

y^{''}+9y=4csc^2(3x)

y^{^{''}} + 9 y = 4 csc^{2} (3 x)

tangent f(x)= 1/(sqrt(8x)),\at x=9

t an g e n t f (x) = \frac{1}{8 x}, at x = 9

(\partial)/(\partial x)(2x^3y^2+2y+4x)

\frac{\partial}{\partial x} (2 x^{3} y^{2} + 2 y + 4 x)

integral of x^3sqrt(x^4+1)

\int x^{3} x^{4} + 1 d x

1/y dx-x/((ln(x))^3)dy=0

\frac{1}{y} d x - \frac{x}{( ln ( x ) ) ^{3}} d y = 0